Deviation Metrics

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array_deviation

Six error/deviation metrics between two arrays: L1, L2, L∞, MAE, MSE, RMSE

Signature

Inputs

aArrayrequired— First array (e.g. reference / truth), flattened to 1-D.
bArrayrequired— Second array (e.g. prediction), flattened to 1-D.

Outputs

l1Scalar— $L_1$ norm of the difference, $\sum |a_i - b_i|$.
l2Scalar— $L_2$ (Euclidean) norm of the difference.
linfScalar— $L_\infty$ (max absolute) deviation.
mean_abs_errScalar— Mean absolute error (MAE).
mean_sq_errScalar— Mean squared error (MSE).
root_mean_sq_errScalar— Root-mean-square error (RMSE).

Description

Deviation Metrics compares two equal-length arrays element-wise and emits six standard error/distance measures at once — three norms of the difference vector and three averaged errors:

$L_{1} = \sum_{i} ∣ a_{i} - b_{i} ∣$ (Manhattan)
$L_{2} = \sum_{i} (a_{i} - b_{i})^{2}$ (Euclidean)
$L_{\infty} = max_{i} ∣ a_{i} - b_{i} ∣$ (worst-case)
MAE $= \frac{1}{n} \sum_{i} ∣ a_{i} - b_{i} ∣$
MSE $= \frac{1}{n} \sum_{i} (a_{i} - b_{i})^{2}$
RMSE $= MSE$

Both inputs are flattened to 1-D, so shape is irrelevant as long as the element counts match. The node is stateless — use it to score a model's fit against ground truth, or to quantify the gap between two signals.

Mathematics

L_{1} = i \sum ∣ a_{i} - b_{i} ∣, L_{2} = i \sum (a_{i} - b_{i})^{2}, L_{\infty} = i max ∣ a_{i} - b_{i} ∣

MAE = \frac{1}{n} i \sum ∣ a_{i} - b_{i} ∣, MSE = \frac{1}{n} i \sum (a_{i} - b_{i})^{2}, RMSE = MSE

Examples

Scoring a prediction

With a = [1,2,3] (truth) and b = [1,2,5] (prediction), the only error is at index 2 ( $∣3 - 5∣ = 2$ ): l1 $= 2$ , linf $= 2$ , l2 $= 2$ , mean_abs_err $= 2/3$ , mean_sq_err $= 4/3$ , root_mean_sq_err $= 4/3 \approx 1.155$ .

Applications

Scoring regression / reconstruction quality against ground truth (RMSE, MAE).
Worst-case tolerance checks via the $L_\infty$ deviation.
Comparing a filtered or compressed signal to its original.

Neat

One evaluation yields both the raw difference-vector norms ($L_1/L_2/L_\infty$) and their per-sample averages (MAE/MSE/RMSE), so scale-dependent and scale-independent views come free together.

$L_\infty$ surfaces the single worst point — invaluable when an average metric hides a localized spike.